1. Find the three cube roots of z = -j and sketch the result in a single Argand plane. (express roots in cartesian form)

Q: 12 3. 5. 13 18 -1 For what value of hs in the plane spanned by j and i? Preview Answers Submit…

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Q: Find parametrizations for the lines in which the planes 5x - 2y = 11, 4y - 5z = -17

A: Given: The given two planes  5x-2y=11 and 4y-5z = -17 are intersects.

Q: Show that the points A = (1, 2), B = (1,0), and C = collinear and express P = (-7,0) in barycentric…

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Q: Use Green's Theorem to calculate ( - sen(a))da + (2a + 3)dy, where C is the triangle with vertices…

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Q: Draw a sketch of the plane of 4x – 4y + 2z – 9 = 0.

A: Solution

Q: Find a parametrization for the line segment beginning at P,(4, - 7,- 7) and ending at P2(0, - 7,2).

A: The line segment beginning at P1<4, -7, -7> and ending at P2<0, -7, 2>

Q: The section of a certain solid cut by any plane perpendicular to the x-axis is a square with the…

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Q: The equation of the plane passing through the point A(8, 10, 9) and orthogonal to the line x = 7+…

A: Given: Point A(8,10,9) Line x=7+8t , y=6+4t , z=5+9t

Q: 2) Calculate the distonce d of the pint ? (-l,(, -2) from the plane passing through the three A(…

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Q: 2. ( eMsa lan--a22 3. All 2-tuples representing points in the first quadrant of the plane including…

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Q: E. Determine the set of points satisfying the condition described by |z – 2i| + |z + 4i| = 10. Then…

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Q: EX Find the reglon in the z-plane represented bye

A: Given

Q: 4- Find The equation ofthe plane That the origin andat the poiat p(u1)ond at is parallel to theline…

A: Equation of plane

Q: Verify that the two planes −3x + 6y + 7z = 1 , 6x − 12y − 14z = 25 are parallel and find the…

A: Given equations of two planes are: -3x+6y+7z=1 and, 6x-12y-14z=25 Thus we can define the normal…

Q: Show that the maximum value of a^2b^2c^2 on a sphere of radius r centered at the origin of a…

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Q: Given that all three points (6, 10, 10), (11, 14, 13), and (k, 8, 6) lie on a plane that contains…

A: If three points lie on the same plane then determinate of matrix made by that points is zero.…

Q: a) Show that the shortest distance between the point (a, b, c) and the plane Ax + By + Cz + D = 0 is…

A: Part(a): Given, The point is a,b,c  And, the plane is, Ax+By+cZ+D=0

Q: 5. Consider two distinct points [b1 in the and plane. Explain why the solutions of the equation det…

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Q: (b) Show that the equation e- - 2:2 = 1 has exactly two solutions in the disk |2| < 1, and that they…

A: Rouche's theorem: Let f and g be holomorphic function in the region D. Suppose gz&lt;fz on the…

Q: Q, : Describe the set of points in the complex plane that satisfy z +1| (2) - = 2 z -1 11-1 =1리 (1)

A: Given that  1)z=z-i2)z+1z-1=2 Find out the set of points

Q: 1. Find an equation for the plane through P,(0,2,–1) perpendicular to n = 3i – 2j-k

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let r() = (In1, 1, 5). Find the equation of the osculating plane corresponding to1 = 1.

A: Find the point at t=1 the vector r(t)=lnt,t,t22 corresponds. lnt,t,t22=ln1,1,122=0,1,12=0,1,0.5…

Q: 23. Through (1,3, 5) and normal to7 - } +k.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: z= 2e'+i

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Q: In Exercises 17-20, find the equation of the plane with the given description.17. Passes through O…

A: Given, A plane passes through O and is parallel to 4x-9y+z=3

Q: Find an equation of the plane satisfying the given conditions.

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Q: 7. If a =i+ 3j – k, b= 2i+ 4j – 2k and c = -i+2j+ 4k, find a number A such that d= a+b+ Ac is…

A: Given a=i+3j-k b=2i+4j-2k c= -i+2j+4k Find the  λ such that d= a+b+λc is parallel to the yz plane…

Q: The section of a certain solid cut by any plane perpendicular to the x-axis is a square with the…

A: Given y^2=9y x^2=9y   a particular solid cut by a plane perpendicular to the x-axis is a square…

Q: Зу — 2z 3D 6

A: Use a graphing utility to plot the plane, 3y-2z=6 .

Q: If a = i+3j – k, b = 2i + 4j – 2k and c = -i + 2j +4k, find a number A such that d = a +b+ Xc is…

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Q: Give equations for two distinct planes whose trace in the xy-plane hasequation 4x + 3y = 8.

A: Given information: The xy-plane has equation 4x + 3y = 8. Calculation: The equation of the plane is…

Q: In the study of plane geometry, certain basic statements called axioms or postulates are accepted as…

A: To check if the statement is true or false

Q: Among all the points on the graph of z = 10-x2 -y² that lie above the plane r+2y+3z = 0, ind the…

A: Given that z=10-x2-y2 and x+2y+3z=0 Find the point which is farthest from the plane.

Q: O Find an equahion for the plane throught (1,-,3) parallel to the plane 3xy+Z=7

A: According to q&amp;a guidelines I can do only 1question

Q: R) show that the pints ACI,l,4), B(2,2,2), c (o,1,5) and D(1,0,5) are coplanear (in the Same plane).

A: Form the three vectors and take the determinant of them. If determinant equal to zero it means all…

Q: Describe the set S of all points in complex plane satisfying Re (2+ i)z +1) > 0

A: Given  inequation is                                                Re(2+i)z+1&gt;0 let…

Q: 1. Find the three cube roots of z =-j and sketch the result in a single Argand plane. (express…

A:

Q: Find the equation of the plane through P(2, – 1,1) that is parallel to Il: 2x + 3y + z – 12 = 0. %3D

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Q: -1. Through (1,5, 2) perpendicular to 37 – J + 4k .

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Q: The part of the plane 3x + 2y +: - 6 that lies in the first octant

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Q: 3 Find the e qu.of Plane that Contains elol; 3) and Parallel to the X-2 Plane and PerPendicular to…

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Q: 16. Find an equation of the plane through the point (1, 1, –2) and parallel to the plane 3r – z =

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Q: Identify the surfaces of equations in the Cartesian form. Show your complete solutions. (a) 2² = 4 +…

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Q: Find points in the Euclidean plane corresponding to the points e₁-[3,-5,-1], e2=[1,-2,2], e3 [2,1,0]…

A: By Pn , we denote the projective space of dimension n, defined as follows: Pn=Rn+1 \ {0}~, where '~'…

Q: 6.) Consider the points P(-1,2,5), Q(2, –3, 0) and (i) Write an equation of the plane containing t

A: Equation of plane: We know that, the equation of plane that passes through point (x, y, z) is given…

Q: Find the distance of the plane passing through the points ā, b, c from the origin.

A: First we derive the vector equation of plane.    The perpendicular distance is the projection on the…

Q: 3. Find all the roots of z³ + 1 = 0 and sketch them on the Argand plane

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Q: Describe your plan for proving the following.

A: Given that AM=MP and ∠AMP=90o. X can be thought of as a plane ground and AM is perpendicular (pole…